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Saturday, February 23, 2013

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I don't agree with your formulation of my problem, which never used the word 'exist'. The relevant predicate in my formulation is 'there is such a thing as ---', or '-- is something'. Here is my formulation

1. a is not a thing any more

2. The predicate '-- is not a thing any more' is satisfied by a.

3. If a relation obtains x and y, then y is a thing

4. (From 2) the relation 'is satisfied by' obtains between the predicate '-- is not a thing any more' and a.

5. (3, 4) a is (still) a thing

6. (1, 5) contradiction.

Presentism is irrelevant. 'What is no longer a thing, is not a thing' is a logical truth, since 'a is no longer a thing' analyses into 'a was a thing and a is not a thing'. Of course, the assumption of premiss (1) involves the assumption of presentism, but if you deny (1), you effectively deny the truth of any proposition like 'there is no such thing as Scollay Square'.

Haecceity properties seem irrelevant. Suppose a* is the haecceity property corresponding to a, and rewrite (1) as 'a* is no longer satisfied by anything'. But premiss (2) is not about a*, the property, but about a, the thing.

So what gives? (3) is a logical truth. So the only thing left to give is (2). We can't explain the truth of past tense propositions where there is no longer any such thing as the subject, in terms of a satisfaction relation between the proposition and the subject. Habeo propositum.

In Bill's formulation:

In B3 the referent of the sentence's subject term is a description which may not be met, but the deduction at B7 assumes that it is. Alternatively, we could say that B3 implicitly assumes that referent-of () is a total function over sentential subject terms. This needs to be proved, or B3 needs an existential assertion in its consequent to the effect that the description is satisfied.

In Ed's formulation:

The converse of E3 is if y is not a thing then no relation holds between x and y. Thus we have no relation to our distant ancestors (who are presumably no longer things), yet the people who are our ancestors are in fact specified by such relations!

>>The converse of E3 is if y is not a thing then no relation holds between x and y. Thus we have no relation to our distant ancestors (who are presumably no longer things), yet the people who are our ancestors are in fact specified by such relations!
<<

Correct. If there is no longer such a thing as Adam, then it is contradictory that I could bear any relation R to Adam. For that would imply I am related by R to something. But we agreed there is no such thing!

One solution would be that the predicate 'there is no such thing as --' is always unsatisfied. Another would be to analyse all relational propositions into propositions referring to present things.

I have it. Clearly we can say "A was the father of B", where A died, but B is still alive. And that is because the relational statement is tensed. What we can't say (I claim) is that any present tense relation holds between A and B, where one of them no longer exists. We can't say (strictly speaking) 'A is the father of B', when A has died.

In summary, the truth of any present tense relational statement ' A is related to B' requires two things, namely A and B, i.e. something must be A and something must be B. But not for a relational statement of the form 'A was related to B'. As long as A was something, and B was something, then the statement can be true.

I was wrong to say this assumes presentism. Quite the opposite. Clearly some things no longer exist, and if presentism is the view that everything exists, then presentism is false. What we can't say, however, is that there are any things that don't exist. I.e. 'Some things no longer exist' does not imply 'there are some things that no longer exist', although it does imply 'there were some things that no longer exist'.

Ed,

In your initial e-mail formulation, I stumbled over 'There is such a thing as ___.' What does that mean exactly? Consider 'There is no such thing as God.' Is that a singular or a general negative existential? Is There is such a thing as God' a singular or a general affirmative existential?

Ed,

'___ is something' is also ambiguous. Peter is something, namely tall. Peter is something, i.e. for some x, x = Peter.

Ed,

Presentism IS relevant. Without presentism, your problem cannot get off the ground.

You are assuming that if a no longer exists, then a in no sense exists. That is not a logical truth, but a substantive proposition in metaphysics. Suppose one maintained that what no longer exists is past, but not, for all that, nonexistent. That would not be a logical contradiction.

>>In your initial e-mail formulation, I stumbled over 'There is such a thing as ___.' What does that mean exactly?
<<

I mean in the common or garden sense of 'there's no such things as unicorns' (general) or 'no such thing as Santa'.

>>You are assuming that if a no longer exists, then a in no sense exists. That is not a logical truth, but a substantive proposition in metaphysics.

No I am not assuming that, because I never used the word 'exists' in my formulation, and deliberately so, precisely to avoid your objection. I am saying that it we can suppose there was something x, but that now there is absolutely no such thing, nothing whatsoever. x has been absolutely annihilated, so that nothing in heaven or earth is identical with that x. I deny existence, in the widest sense of existence, to x.

>>Without presentism, your problem cannot get off the ground.

It depends on what you mean by presentism. I take it to be the proposition that everything exists now. I deny this. Clearly some things (Socrates) do not exist any more. Some things do not exist. Equally, I deny that there are any things that do not exist. You need to get your head round that. I.e. both are true:

(A) Some things do not exist.
(B) There is nothing that does not exist.

>>Suppose one maintained that what no longer exists is past, but not, for all that, nonexistent. That would not be a logical contradiction.

Surely it is a logical contradiction, depending on your definition of 'no longer exists'. My definition is as follows

(1) x no longer exists =def x existed and x does not exist

Therefore

(2) what no longer exists is what existed but does not exist

and assuming

(3) x does not exist =def x is nonexistent

then it follows that your statement "what no longer exists is past, but not, for all that, nonexistent" contains a contradiction.

Hi Ed,

I think you have it too. I have a minor quibble but this looks like real progress. A is/was related to B implies A is/was and (B is or B was).

I think we can restate what you are saying in terms of ∃. We must read '∃x.phi(x)' as 'for some thing temporarily called x, phi (x)' We must NOT read it as 'there exists an x such that...' or as 'there is an x such that...' The main verb is in the phi not the ∃ and may be tensed. Quantification, by default, is over the things that were or are. 'There is something that phis' translates to '∃x. x is and phi(x)'. So 'there is something that does not exist' translates to '∃x. x is and not x is' which is contradictory, hence false. Hence I agree with your (B) that there is nothing that does not exist. Your (A), 'some thing does not exist', follows by existential generalisation from 'Socrates does not exist'. As you imply, it takes a little practice to get used to this distinction.

Unfortunately, E3 becomes If a relation obtains [between?] x and y, then y is a thing or y was a thing and this vitiates your argument.

I agree regarding 'presentism'.

David: you have it. Precisely.

Ed,

I think you are confusing presentism with what Russell called solipsism of the present moment.

>>Ed, I think you are confusing presentism with what Russell called solipsism of the present moment.

Can you give me a working definition of presentism then?

In any case (and returning to the original topic), I don’t see how presentism is relevant to the problem I outlined above. Here it is again (wording changed to clarify against certain objections)

1. There is no such thing as Caesar any more

2. The predicate 'there is no such thing as -- any more' is satisfied by Caesar.

3. If a relation obtains x and y, then there is such as thing as y

4. (From 2) the relation 'is satisfied by' obtains between the predicate '-- is not a thing any more' and Caesar.

5. (3, 4) There is such a thing as Caesar.

6. (1, 5) contradiction.

Premiss (1) is Moorean. There is no longer any such thing or person as Caesar. (Or if you dispute that for reason of immortality of Caesar, choose some mortal or perishable object). (2) is a theoretical. (3) is a logical truth, and the rest is also logic. You must choose between (1) and (2), i.e. choose between a Moorean truth, and a dubious theoretical assumption.

Bill,

You published the first comment I made this morning, but not the second. I felt the second was more important. I claimed that the proposition

(*) There is no such thing as Caesar.

is Moorean. Moreover, I claimed the truth or falsity of Presentism is irrelevant to whether it was true. Presentism is a substantive metaphysical thesis, whereas the proposition that there is no such thing (or person) as Caesar is not metaphysically substantive, nor is it a thesis but a historical fact.

I'll take this up again in a separate post.

Ed and Bill,

Would you agree that '_was born on the same day of the year as_' defines a bona fide relation between individuals? Orlando Gibbons was born on the same day of the year as Isaac Newton (Christmas day actually), so surely we are entitled to say that said relation holds between Gibbons and Newton, though neither exists any longer? What does this make of Ed's 'logical truth' (3)?

1 and 5 are not contradictory.

Obviously we can remove any two proper names from a sentence, e.g. "— died in 1654 and – is still alive" and get one of these fake Fregean relational expressions. Precisely what I am denying is that these necessarily express genuine relations.

On the definition of presentism, Ned Markosian's article http://plato.stanford.edu/entries/time on Time says that according to presentism “if we were to make an accurate list of all the things that exist — i.e., a list of all the things that our most unrestricted quantifiers range over — there would be not a single non-present object on the list”. I am not sure whether to agree with this or not. I hold that, if we were to make an accurate list of all the things that exist, or which used to exist, then the list would contain the names of objects which are not present.

>>1 and 5 are not contradictory.

1 is ‘There is no such thing as Caesar any more’. The definition I am using for this sentence is ‘there was such a thing as Caesar and there is not such a thing as Caesar’. Thus

1A there was such a thing as Caesar and there is not such a thing as Caesar (definition of 1)

1B there is not such a thing as Caesar (& elimination)

This contradicts 5 (‘there is such a thing as Caesar’).

>> Obviously we can remove any two proper names from a sentence, e.g. "— died in 1654 and – is still alive" and get one of these fake Fregean relational expressions.

But Ed, that's exactly the move you are making in going from your (2) to your (4). What criterion have you got to show that my 'has same birthday as' relation is fake and your 'satisfies' relation is genuine?

For me xRy <---> Px & Qy defines a perfectly good binary relation. So what if it factors into two monadic relations? It may be boring and useless but it's still a two-place truth function.

Besides, the birthday relation doesn't factor this way so it's a bit more interesting. You would presumably agree that '_was shorter than_' and '_was taller than_' are archetypical relations? '_was as tall as_' is a logical construction from these. The birthday example has the same form.

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